ON COMPACT ANISOTROPIC WEINGARTEN HYPERSURFACES IN EUCLIDEAN SPACE

Julien Roth (1) , Abhitosh Upadhyay (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IISc - Indian Institute of Science

We show that, up to homotheties and translations, the Wulff shape W F is the only compact embedded hypersurface of the Euclidean space satisfying H F r = aH F + b with a 0, b > 0, where H F and H F r are respectively the anisotropic mean curvature and anisotropic r-th mean curvature associated with the function F : S n −→ R * +. Further, we show that if the L 2-norm of H F r − aH F − b is sufficiently close to 0 then the hypersurface is close to the Wulff shape for the W 2,2-norm.

Domaines: Géométrie différentielle [math.DG]

Julien Roth, Abhitosh Upadhyay. ON COMPACT ANISOTROPIC WEINGARTEN HYPERSURFACES IN EUCLIDEAN SPACE. Archiv der Mathematik, 2019, 113 (2), pp.213-224. ⟨10.1007/s00013-019-01315-8⟩. ⟨hal-01985969⟩